L'interpolazione razionale e la sua validità

Abstract

The rational interpolation can be used to correct anomalous values or to add missing values in a distribution of n points. Applying this method it is possible to identify a function passing by any n given points. The function is given by F(x)=S(x)/T(x) where S(x) and T(x) are two rational polynomials in x whose degrees depend on n. In this paper we present an interpolating method and we evaluate the statistical validity of the method here developed with specific application to economical, clinical and environmental data. The results show that the discrepancy between the actual value and the estimate of the same value obtained applying the rational interpolation is lower than 0,1 in 74,5% and 67,6% of cases using respectively economical and environmental data, while using clinical data the discrepancy is lower than 1 in 91% of cases.